多项式的阶

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

When to get the coefficients of polynomial directly,the ill-conditioned matrix may be produced and effect the precision of result.Using orthogonal polynomial can avoid this problem.This paper introduces 4 orthogonal polynomial.In our discussion,it is proposed to use Chebyshev polynomial and Legendre polynomial,they are easier to sa...

讨论4种常用正交多项式在拟合卫星轨道与时间函数时的适用性；通过计算实例说明利用切比雪夫多项式和勒让德多项式做数据拟合时具有很高的精度；分析得出评定多项式拟合数据精度的适用阶数，实际应用中可降低工作量，提高计算效率；最后讨论同一多项式阶数下不同历元数对拟合结果的影响。

In allusion to dynamic nonlinear large-scale industrial processes, to bring up gained the method of decentralized identification for the strong consistency estimates of the divisible steady-state models, it is used that property of polynomial can infinitely approach to the nonlinear function and in optimization processes use step signals as input signals, the divisible steady-state models of dynamic nonlinear large-scale industrial processes, and the cognizable conditions are obtained.

针对动态非线性大工业过程，提出了得到其可分稳态模型强一致性估计的分散辨识方法；利用多项式对非线性函数的无限逼近的性质和优化过程中设定点的阶跃信号作输入激励信号，获得了动态非线性大工业过程的可分稳态模型和可辨识的条件。

Since the information for the generalized Jordan canonical blocks in the generalized Jordan canonical form can not be easily obtained from the characteristic polynomial and the commutative law does not hold for matrix multiplication,we compute the common form of the power of the generalized Jordan canonical form and get a concise expression for the power of the defective matrix.

考虑到不易从它的特征多项式获得构成广义若当标准型的阶数更小的广义若当块的有关信息，针对矩阵乘法不满足交换率，本文从计算广义若当标准型的幂的一般形式出发，获得实数域上亏损矩阵的幂的一个简洁表示。

In Chapter 1,some elementary knowledge was introduced,such as theBernstein-Bezier representation for polynomials,conform triangulation,theconditions of convexity for Bézier spline surfaces,the funtional andgeometric continuity condition for neibour Bézier surface patches etc.,specially,based on the Liu-Ding-Yuan Theorem for geometric continuity,some simple and practical conditions were obtained.

第一章介绍一些基本知识，如多项式的Bernstein-Bézier表示，相容三角剖分的定义，Bézier三角样条曲面保凸的条件，相邻Bézier曲面片函数连续和几何连续的条件等，特别地，在刘鼎元关于几何连续条件的一般定理的基础上，导出了几个较简单的实用的一阶几何连续条件。

In this paper, it develops a novel decentralized adaptive fuzzy control for a class of large-scale nonlinear systems with higher order interconnections.

针对一类关联项的上界是高阶多项式的关联大系统，设计了一种新的分散自适应模糊控制方法。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

Graph′s depth first search recursive algorithm and n-order Legendre polynomial recursive algorithm are to equivalent non-recursive algorithms.

利用该组规则将图的深度优先搜索和n阶勒让德多项式的递归算法转换成了等价的非递归算法。

A method of the order selection of polynomial model for geometric errors modeling for NC machine tool was presented.

提出了一种针对数控机床几何误差多项式模型的阶数选择方法。

The orthogonal polynomials order of effective waves is confirmed according to the energy variation with order increasing. This method can not only attenuate the noise but also preserve the AVO properties.

相对于固定阶次的基于正交多项式变换压制噪声的方法，所提出的方法根据能量随阶次变化的规律，自适应确定表达有效信号的正交多项式阶次，既提高了信号和噪声的分离效果，又有效地保护了地震信号中的AVO信息。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。